Question

2．計(jì)算：|1-$\frac{1}{2}$|+|$\frac{1}{2}$-$\frac{1}{3}$|+|$\frac{1}{3}$-$\frac{1}{4}$|+…+|$\frac{1}{9}$-$\frac{1}{10}$|

Answer 1

分析 先去掉絕對(duì)值，再利用有理數(shù)的加減法進(jìn)行計(jì)算．

解答 解：|1-$\frac{1}{2}$|+|$\frac{1}{2}$-$\frac{1}{3}$|+|$\frac{1}{3}$-$\frac{1}{4}$|+…+|$\frac{1}{9}$-$\frac{1}{10}$|
=$1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+…+\frac{1}{9}-\frac{1}{10}$
=1-$\frac{1}{10}$
=$\frac{9}{10}$．

點(diǎn)評(píng) 此題考查有理數(shù)的加減混合計(jì)算，關(guān)鍵是根據(jù)絕對(duì)值的定義化簡再計(jì)算．